Multiscale analysis in Lagrangian formulation for the 2-D incompressible Euler equation
We perform a systematic multiscale analysis for the 2-D incompressible Euler equation with rapidly oscillating initial data using a Lagrangian approach. The Lagrangian formulation enables us to capture the propagation of the multiscale solution in a natural way. By making an appropriate multiscale expansion in the vorticity-stream function formulation, we derive a well-posed homogenized equation for the Euler equation. Based on the multiscale analysis in the Lagrangian formulation, we also derive the corresponding multiscale analysis in the Eulerian formulation. Moreover, our multiscale analysis reveals some interesting structure for the Reynolds stress term, which provides a theoretical base for establishing systematic multiscale modeling of 2-D incompressible flow.
© 2005 American Institute of Mathematical Sciences. Received: November 2004; Revised: March 2005; Available Online: September 2005. This work was supported in part by an NSF FRG grant DMS-0353838 and an NSF ITR grant ACI-0204932. The second author also was supported in part by an NSF grant DMS-0073916, Major State Basic Research Program of P. R. China grant G1999032803, and the Research Fund for Doctoral Program of High Education by China State Education Ministry.
Published - 10_3934_dcds_2005_13_1153.pdf